Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides

TL;DR

This paper analytically investigates nonlinear light behaviors near phase transition in non-PT-symmetric waveguides, revealing the existence of solitons and amplitude oscillations, with some waveguides showing intensity amplification regardless of phase transition status.

Contribution

It introduces an analytical framework using multi-scale perturbation methods to predict nonlinear phenomena in non-PT-symmetric waveguides near phase transition, extending understanding beyond PT-symmetric systems.

Findings

Support for continuous soliton families above and below phase transition.

Robust amplitude-oscillating solutions in certain waveguides.

Intensity amplification in some waveguides regardless of phase transition.

Abstract

Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that the first class of these non-PT-symmetric waveguides support continuous families of solitons and robust amplitude-oscillating solutions both above and below phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity even if the waveguide is below phase transition. These analytical predictions are confirmed by direct computations of the full system.